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SPLITTING INVARIANT SUBSPACES IN THE HARDY SPACE OVER THE BIDISK
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 102 / Issue 2 / April 2017
- Published online by Cambridge University Press:
- 12 May 2016, pp. 205-223
- Print publication:
- April 2017
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- Article
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Let
$H^{2}$ be the Hardy space over the bidisk. It is known that Hilbert–Schmidt invariant subspaces of 
$H^{2}$ have nice properties. An invariant subspace which is unitarily equivalent to some invariant subspace whose continuous spectrum does not coincide with 
$\overline{\mathbb{D}}$ is Hilbert–Schmidt. We shall introduce the concept of splittingness for invariant subspaces and prove that they are Hilbert–Schmidt.
